Strongly fillable contact 3–manifolds without Stein fillings
Geometry & topology, Tome 9 (2005) no. 3, pp. 1677-1687.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We use the Ozsváth–Szabó contact invariant to produce examples of strongly symplectically fillable contact 3–manifolds which are not Stein fillable.

DOI : 10.2140/gt.2005.9.1677
Keywords: contact structure, symplectically fillable, Stein fillable, Ozsváth–Szabó invariant

Ghiggini, Paolo 1

1 CIRGET, Université du Québec à Montréal, Case Postale 8888, succursale Centre-Ville, Montréal (Québec) H3C 3P8, Canada
@article{GT_2005_9_3_a11,
     author = {Ghiggini, Paolo},
     title = {Strongly fillable contact 3{\textendash}manifolds without {Stein} fillings},
     journal = {Geometry & topology},
     pages = {1677--1687},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2005},
     doi = {10.2140/gt.2005.9.1677},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2005.9.1677/}
}
TY  - JOUR
AU  - Ghiggini, Paolo
TI  - Strongly fillable contact 3–manifolds without Stein fillings
JO  - Geometry & topology
PY  - 2005
SP  - 1677
EP  - 1687
VL  - 9
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2005.9.1677/
DO  - 10.2140/gt.2005.9.1677
ID  - GT_2005_9_3_a11
ER  - 
%0 Journal Article
%A Ghiggini, Paolo
%T Strongly fillable contact 3–manifolds without Stein fillings
%J Geometry & topology
%D 2005
%P 1677-1687
%V 9
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2005.9.1677/
%R 10.2140/gt.2005.9.1677
%F GT_2005_9_3_a11
Ghiggini, Paolo. Strongly fillable contact 3–manifolds without Stein fillings. Geometry & topology, Tome 9 (2005) no. 3, pp. 1677-1687. doi : 10.2140/gt.2005.9.1677. http://geodesic.mathdoc.fr/articles/10.2140/gt.2005.9.1677/

[1] F Ding, H Geiges, Symplectic fillability of tight contact structures on torus bundles, Algebr. Geom. Topol. 1 (2001) 153

[2] Y Eliashberg, Filling by holomorphic discs and its applications, from: "Geometry of low-dimensional manifolds, 2 (Durham, 1989)", London Math. Soc. Lecture Note Ser. 151, Cambridge Univ. Press (1990) 45

[3] Y Eliashberg, Unique holomorphically fillable contact structure on the 3–torus, Internat. Math. Res. Notices (1996) 77

[4] Y Eliashberg, A few remarks about symplectic filling, Geom. Topol. 8 (2004) 277

[5] J B Etnyre, K Honda, On the nonexistence of tight contact structures, Ann. of Math. $(2)$ 153 (2001) 749

[6] J B Etnyre, K Honda, Tight contact structures with no symplectic fillings, Invent. Math. 148 (2002) 609

[7] P Ghiggini, Ozsváth–Szabó invariants and fillability of contact structures, Math. Z. 253 (2006) 159

[8] E Giroux, Une infinité de structures de contact tendues sur une infinité de variétés, Invent. Math. 135 (1999) 789

[9] R E Gompf, Handlebody construction of Stein surfaces, Ann. of Math. $(2)$ 148 (1998) 619

[10] M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307

[11] P B Kronheimer, T S Mrowka, Monopoles and contact structures, Invent. Math. 130 (1997) 209

[12] P Lisca, G Matić, Tight contact structures and Seiberg–Witten invariants, Invent. Math. 129 (1997) 509

[13] P Lisca, A I Stipsicz, Tight, not semi-fillable contact circle bundles, Math. Ann. 328 (2004) 285

[14] P Lisca, A I Stipsicz, An infinite family of tight, not semi-fillable contact three-manifolds, Geom. Topol. 7 (2003) 1055

[15] P Ozsváth, Z Szabó, Heegaard Floer homology and contact structures, Duke Math. J. 129 (2005) 39

[16] P Ozsváth, Z Szabó, Holomorphic triangles and invariants for smooth four-manifolds, Adv. Math. 202 (2006) 326

[17] P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179

[18] P Ozsváth, Z Szabó, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. $(2)$ 159 (2004) 1159

[19] P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. $(2)$ 159 (2004) 1027

[20] O Plamenevskaya, Contact structures with distinct Heegaard Floer invariants, Math. Res. Lett. 11 (2004) 547

Cité par Sources :